To find the value of y in the system of equations 3x + 5y = 1 and 7x + 4y = 13, we can use either the substitution method or the elimination method. For this explanation, we’ll use the elimination method.
Step 1: Align the equations
We have the following equations:
- 1. 3x + 5y = 1
- 2. 7x + 4y = 13
Step 2: Eliminate one variable
To eliminate one variable, we need to manipulate the equations. Let’s multiply the first equation by 7 and the second by 3 so we can align the coefficients of x:
- 7(3x + 5y) = 7(1) -> 21x + 35y = 7
- 3(7x + 4y) = 3(13) -> 21x + 12y = 39
This gives us:
- 1. 21x + 35y = 7
- 2. 21x + 12y = 39
Step 3: Subtract the second equation from the first
Now, we subtract the second equation from the first to eliminate x:
(21x + 35y) – (21x + 12y) = 7 – 39
Which simplifies to:
23y = -32
Step 4: Solve for y
Now, we can solve for y:
y = -32/23
Therefore, the value of y in the solution to the system of equations is: -32/23.
Final Result: The value of y is -32/23.